Space of modular forms of level 2320, weight 1, and Character 2320.bj

• Label: 2320.1.bj
• Level: $2320$
• Weight: $1$
• Character orbit: 2320.bj
• Rep. character: $\chi_{2320}(1409,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $360$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2320.bj (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(360\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2320, [\chi])\).

	Total	New	Old
Modular forms	36	6	30
Cusp forms	12	2	10
Eisenstein series	24	4	20

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{11} + 2 q^{19} - 2 q^{25} - 2 q^{31} + 2 q^{41} + 2 q^{45} + 2 q^{49} + 2 q^{55} + 2 q^{61} + 2 q^{79} - 2 q^{81} - 2 q^{89} + 2 q^{95} - 2 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2320, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2320.1.bj.a	$2320$	$1$	2320.bj	145.f	$4$	$2$	$1$	$1.158$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{5}) \)			✓	✓	145.1.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-i q^{5}+i q^{9}+(i+1)q^{11}+(i+1)q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2320, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2320, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 5}\)